From DE 299 80 181 U1, an adapting machine with a clamping device for the clamping of a rotating machine element is known. The clamping device contains a main body with a centric retaining opening for the machine element and a chuck actuating unit for a collet chuck, which can be adjusted axially relative to the main body. In this known clamping device of a balancing machine, the machine element is held by claw-shaped clamping elements on the collet chuck in the tool holder. For the clamping, the clamping elements of the collet chuck are supported on a bearing surface of an actuating head of a chuck actuating unit. The chuck actuating unit is supported in a main part body by means of a rolling contact bearing, and the main part body is, in turn, screwed to the main body. By means of such a connection and the many connection sites between the bearing surface for the clamping elements and the main body, however, problems with the centering may arise, which can have a negative effect on the concentricity of the tool holder.